Position measuring transformer having multiple independent sections for reduction of measurement errors

ABSTRACT

A method and apparatus for measuring linear and rotary positions with position measuring data elements, such as position measuring transformers, where the data elements are affected by errorcausing conditions such as eccentricity and skew. Measurements are made so as to avoid the compound effects of eccentricity and skew by dividing the conventional, continuous space-quadrature windings appearing on one member of the transformer, into a plurality of windings groups where the continuous winding of the other member remains unchanged. Each group typically includes a plurality of inter-connected sine and a plurality of interconnected cosine winding sections where those winding sections are in space-quadrature of the pole cycle of the continuous winding. The measurements made from each group, in one embodiment, are averaged to form a highly error-free resultant measurement. In another embodiment, the difference between group measurements are employed to form a measurement of the eccentricity of one member with respect to the other.

United States Patent Tripp et a].

[451 June 27, 1972 [54] POSITION MEASURING TRANSFORMER HAVING MULTIPLEINDEPENDENT SECTIONS FOR REDUCTION OF MEASUREMENT ERRORS PrimaryExaminer-John W. Caldwell Assistant Examiner-Robert J. MooneyAttomey--WiIIiam E. Beatty and David E. Lovcjoy [57] ABSTRACT [72]Inventors: Robe Tripp Tuckahoe; Robert A method and apparatus formeasuring linear and rotary posi- Geuer wamagh both of tions withposition measuring data elements, such as position 73 Assignee;lndudosyn CQWGOII, New York, measuring transformers, where the dataelements are affected by error-causing conditions such as eccentricityand skew. [221 Flled: 1970 Measurements are made so as to avoid thecompound effects 21 App] 77 7 5 of eccentricity and skew by dividing theconventional, continuous space-quadrature windings appearing on onemember of the transformer, into a plurality of windings groups where[52] U.S. CI. ..340/ 198, 340/195, 340/347 SY, the continuous winding ofthe other member remains 5 I t Cl 336/ unchanged. Each group typicallyincludes a plurality of interconnected sine and a plurality ofinter-connected cosine wind- [58] Field Search "340/ ing sections wherethose winding sections are in space-quadrature of the pole cycle of thecontinuous winding. The measurements made from each group, in oneembodiment, are [56] Reta-ems Cited averaged to form a highly error-freeresultant measurement.

UMTED STATES PATENTS In another embodiment, the difference between groupmeasurements are employed to form a measurement of the eccen- 3,235,78 I2/1966 Spencer ..340/ I96 tricity f one member with respect to theother, 3,555,542 1/1971 Guiot ...340/198 3,562,740 2/l97I Watkins..340/l98 17 Claims, 11 Drawing Figures [10 COMPUTER /7 2 DISPLAY I i 1l 9 4 I 4| COARSE POSITION 3o APPARATUS T COARSE ,9 13 o FIN E 4 ,u l lCONTROL 2 i 20 l7 Q m SWITCHING COUNTER D/A AND -Y Z CONVERTER COUPLINGI6 1 NETWORK I9 w 15 A I GROUP 22 SELECTOR 45- DRIVE l 44 SERVO cou 'rEREADOUT SW'TCH CONTROL PATENTEDJum I972 SHEET 10F 5 [IO COMPUTER /7DISPLAY 1 l COARSE POSITION 3o APPARATUS COARSE I 0 FINE CON 2 2e 1 20 lw (Y) 3 \FILTER [JP/DOWN SWITCHING ["COUNTER D/A AND Z CONVERTER LING ZNETWORK 23 k 4 l9 25 GROUP I 22 I SELECTOR 43 DRIVE L 48 I4 36 47 SERVOCOUNTER READOUT SWITCH 1% CONTROL FIG. 40

INVENTORS ROBERT W. TRIPP ROBERT Z. GELLER ATTO R N P'ATENTEnJum m2 sawu or s FIG. 6

FIG. 7b

POSITION MEASURING TRANSFORMER HAVING MULTIPLE INDEPENDENT SECTIONS FORREDUCTION OF MEASUREMENT ERRORS BACKGROUND OF THE INVENTION The presentinvention relates to data elements for indicating and measuring rotaryor linear positions. Typical data elements for such measurements areposition measuring transformers of the type manufactured under thetrademark Inductosyn. Specifically, the present invention relates toimproved measurement methods and apparatus employing position measuringdata elements.

Position measuring transformers usually have one member including asingle continuous winding inductively coupled to two space-quadraturewindings on another member. The inductive coupling between members is afunction of the mechanical displacement (rotational of translation) ofone member relative to the other member. The windings on the members aretypically comprised of a plurality of conductor bars which extendtransverse to the direction of relative movement of the two members. Theconductor bars forming the space-quadrature windings on one member arein spacequadrature of the pole cycle of the conductor bars on thecontinuous winding of the other member. Those space-quadrature windingsare typically identified as sine and cosine windings.

Improvement in the accuracy and operation of position measuringtransformers is a continual objective. One prior art position measuringtransformer which reduces errors caused by eccentricity and skew of thewinding patterns in U.S. Pat. No. 2,799,835 entitled Position MeasuringTransformers, invented by R. W. Tripp et a1. and assigned to the sameassignee as the present invention. The error reduction in that patent isachieved by maintaining a specified ratio Of conductor bar width withrespect to .the space between conductor bars, use of a different pitch(periodicity) of the winding on one member with respect to the windingson the other member, and other techniques.

Another prior art position measuring transformer having improvedaccuracy employs multi-layer windings wherein the cofunction windings onone layer are arranged in the gaps of cofunction windings on the otherlayer so as to present the appearance of substantially a continuouswinding. Such a transducer is described in US Pat. No. 3,441,888 to C.L. Farrand, assigned to the same assignee as the present invention.

The tyPes of errors usually attendant position measuring transformersare described in the article Inductosyn Angular Readout System of theUS. Naval Observatory 6-inch Transit Circle, 1969 Proceedings ofElectro-Optical Systems Design Conference, pp. 634-641. As indicatedtherein and as is otherwise known (e.g. the above-noted US. Pat. No.2,799,835) the mechanical misalignment of the two relatively movablemembers of a position measuring transformer gives rise, in the case of arotary device, to an error that has a cycle of 360 mechanical degreesand hence is termed a once-perrevolution error. Perfectly alignedtransducers have no errors but, of course, mechanical misalignment fromimperfect mountings, bearings, and transducer plates always gives riseto errors of some degree.

These errors arising from mechanical misalignment are generallyclassified for rotary devices as errors due to eccentricity and errorsdue to skew. Eccentricity is a measure of the displacement of thecenters of the rotor or stator windings with respect to the axis ofrotation of the rotor. This eccentricity causes an asymmetry whichvaries the coupling between stator and rotor windings as a function ofdifferent positions of the rotor with respect to the stator. Skew is ameasure of the non-orthogonality of the rotor and stator planes withrespect to the axis of rotation of the rotor. This nonorthogonalitycauses the air gap to vary as a function of different rotor positionswith respect to the stator.

While the prior art techniques employed in minimizing errors have beenhighly successful for general applications,

Such an application is in the accurate measurement and tracking of starsas carried out, for example, at the United States Naval Observatory asoutlined in the above-referenced article. In such accurate applications,the compound effects of skew and eccentricity become of appreciablesignificance. While analyses of skew alone and eccentricity alone havebeen carried out and techniques for eliminating errors caused by theseconditions separately are known, the compound efiects still havepresented errors which are undesirable.

SUMMARY OF THE INVENTION The present invention provides methods andapparatus for improved measurements of linear and rotary positions wherethe effects of eccentricity, skew and other similar error-causingconditions attendant position measuring data elements are reduced and,in some cases, the conditions are measured.

In the present invention, measurements are made with position measuringtransformers having their conventional, singular windings divided into aplurality of winding groups, such as four quadrants, where each group isindependently operated to produce independent measurements. Each grouptypically includes a plurality of sine and a plurality of cosine relatedwinding sections. In the case of four groups, four measurements ratherthan the conventional one are obtained. Each of those four measurements,one for each group, may be combined to form a resultant measurementwhich is less affected by errors resulting from the compound effects ofeccentricity and skew than the conventional single measurement.

In accordance with one embodiment of the present invention, themeasurements from each group are independently made and then averaged toform a resultant measurement which is more accurate than if all of thegroups were serially inter-connected in a conventional manner to obtainthe usual one measurement.

In accordance with another embodiment of the invention, differencesbetween group measurements are employed to form a measure of theconditions causing errors.

A specific stator-energization embodiment of the invention employs arotary position measuring transformer for measuring the space angle Xbetween the transformer rotor and stator. The stator windings aredivided into four groups, called quadrants, where each quadrant includesa sine winding and a cosine winding formed of sine and cosine windingsections, respectively. In operation, the transformer is employed in asystem which may be operated in a readout mode to measure the spaceangle X or in a servo mode to command movement to the space angle X.Considering the readout mode by way of example, input signals having atrigonometric relation to an electrical angle Y are applied to the sineand cosine windings of the stator in one quadrant to induce an outputsignal in the continuous winding on the rotor proportional to sin(X-Y).That output signal is employed, using a digital counter for storing arepresentation of Y and a digital-to-analog converter for generating theinput signals, to alter the input signals until the output signaldeveloped is reduced to a null as occurs when the electrical angle Y isequal to and is therefore a measure of the space angle X. The value ofY, as appearing in the digital counter, is recorded as the measurementof the space angle X for the first group. Thereafter, the steps arerepeated for each of the other three quadrants of the stator so as toobtain three more measurements of the space angle X. Thereafter, thefour measurements of the space angle X are averaged to provide a highlyaccurate resultant measurement of the space angle X.

In a further embodiment of the present invention in which four groupsare employed, the difference between the measurements in the first andthird quadrants is obtained to form a measure of the eccentricitycomponent along a first axis bisecting the second and fourth quadrants.Similarly, the difference between the measurements from the second andfourth quadrants are determined to form a measure of the eccentricitycomponent along a second axis, at right angles to there are occasionswhen even greater accuracy is desired. the first axis, bisecting thefirst and third quadrants.

In a rotor-energization embodiment of the present invention, the rotoris energized with a constant amplitude AC signal so as to introduce in aplurality of stator winding groups sin(X) and cos(X) signals for eachgroup, where the space angle X is the same as in the previousembodiment. The sin(X) and cos(X) signals, for each group, are suppliedto a sine/cosine computer network which is controlled by an electricalangle Y so as to form a resultant signal output proportional tosin(X-Y). This rotor energization embodiment may also be employed in theservo and readout modes described above. Specifically, during thereadout mode, the space angle X is held constant and the electricalangle Y is varied until the resultant signal from the computer networkis a null as occurs when X equals Y. Similarly, the servo operation iscarried out by holding the commanded input electrical angle Y a constantand varying the space angle X (by mechanically turning the rotor) againuntil the resultant signal from the computer network is a null as occurswhen X equals Y.

The foregoing and other objects, features, and advantages of theinvention will be apparent from the following more particulardescription of the preferred embodiments of the invention, asillustrated in the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 depicts an apparatus in which aposition measuring transformer is employed in servo and readout modesfor position commanding and position measurement, respectively, andwhere the transformer stator windings are divided into and are energizedby groups.

FIG. 2 depicts a schematic top view representation of the windings of aposition measuring transformer, like that employed in FIG. 1, showingthe relationship between the two windings in quadrature and thecontinuous winding.

FIG. 3 is a front view of the superposed windings of FIG. 2 showing theparallel relationship of the planes and the concentricity of the windingpatterns.

FIG. 4(a) depicts the apparatus of FIG. 2, with a schematic front viewlike FIG. 3, wherein the centers of the windings are displaced so as tocreate a condition of eccentricity.

FIG. 4 (b) depicts the position measuring transformer of FIG. 2 with aschematic front view wherein the centers are concentric but wherein theplanes are non-parallel so as to introduce skew.

FIG. 4(a) depicts a schematic front view of the FIG. 2 transfonner inwhich the eccentricity condition of FIG. 4(a) and the skew condition ofFIG. 4(b) exist simultaneously.

FIG. 5 depicts, in further detail, the switching and coupling network ofFIG. 1 connected to a position measuring transformer.

FIG. 6 represents a schematic view of the space shifts of four windingsections which are explanatory of the shifts occuring in the eightstator winding sections of FIG. 2 as a result of eccentricity like thatdepicted in FIG. 4(a).

FIG. 7(a) and 7(b) represent schematic views of the space shifts of fourwinding sections which are explanatory of the shifts occuring in theeight stator winding sections of FIG. 2 when skewed in the manner ofFIG. 4(b).

FIG. 8 depicts an alternate embodiment of the present invention againoperable in servo and readout modes for positioning and measurement,respectively, where the rotor is energized to induce signals in groupsof stator DETAILED DESCRIPTION An apparatus for energizing independentwinding groups of a position measuring transformer is generally depictedin FIG. 1. The apparatus of FIG. 1 is operational in two modesconveniently called the servo mode and readout mode. Servo and ReadoutModes In the servo mode,an electrical signal in the form of a constantcommand electrical angle Y is supplied to the stator 2 of the positionmeasuring transformer l and the rotor 3 of position measuringtransformer 1 is mechanically driven until the space angle X, measuringthe relative position of rotor 3 with respect to stator 2, equals theelectrical angle Y and therefore generates a null or zero voltagesignal. In the readout mode, the reverse operation occurs in that thespace angle X of the rotor serves as the constant input and theelectrical angle Y is driven electrically until the resultant signalfrom the rotor is a null as occurs when X equals Y.

The servo and readout modes of operation of position measuringtransformers are typically described in U.S. application, Ser. No.809,533, filed 3/24/69, entitled Position Measuring System, and U.S.Pat. No. 3,514,775 entitled DIGITAL-TO- ANALOG CONVERTER both assignedto the same assignee as the present invention.

In the servo mode, the apparatus of FIG. 1 commands the rotor to a spaceangle and the rotor is driven until it assumes that position. Inoperation, a conventional digital computer 10 issues the initial commandas a digital representation of the desired angular position of the rotor3. The digital representation is transferred to an up/down counter 15.Counter 15 may be any conventional binary or other digital counteradapted and controlled for recording the desired position of rotor 3.The digital command in counter 15 is conveyed to a digital-toanalog(D/A) converter 17. D/A converter 17 converts the digital signal fromline 16 to analog signals on lines 18 and 19. Lines 18 and 19 aretypically designated sine and cosine lines because the signals thereon,while being of the same time phase, have amplitudes which areproportional to the sine and to the cosine, respectively, of the sameelectrical angle Y where the angle is related to the position of rotor3. In conventional operation, lines 18 and 19 are connected directly,through suitable coupling devices such as transformers, to the stator 2of transformer 1.

D/A converter 17 is typically like that disclosed in U.S. Pat. No.2,849,668 assigned to the same assignee as the present invention.Counter 15 herein performs the switch selection (e. g. 105, FIG. 7therein) function of the tape reader therein in a conventional manner.The sin and cos outputs (FIG. 7 therein) are analogous to the sine andcosine lines 18 and 19 herein. An alternative D/A converter suitable foruse in the present invention is disclosed in the applicationTrigonometric Signal Generator And Machine Control, Ser. No. 864,079,filed 10/6/69, by R. W. Tripp and assigned to the same assignee as thepresent invention.

In accordance with the present invention, the sine and cosine signals onlines 18 and 19 are connected to a stator 2 through switches inswitching and coupling network 20. Network 20 allows the sine and cosinesignals on lines 18 and 19, under the control of groups selector 21, tobe applied to predetermined winding groups on the stator 2. The network20 functions, in one specific embodiment of the invention, to convertthe pair of sine and cosine signals from lines 18 and 19 to four pairsof independently energizable sine and cosine signals schematicallyrepresented by the four pairs of lines 22. The lines 22 are connected towinding groups on the stator 2 of the transformer 1 in a mannerdescribed in more detail hereinafter.

The input signals applied via the lines 22 to the stator 2 of positionmeasuring transformer 1 induce a signal in the rotor 3 which is afunction of the space angle X of the rotor 3 with respect to the stator2 and the electrical angle Y of the signals applied via lines 22. Theresultant signal from the rotor 3 is generally a function of sin( X-Y).That resultant signal is conveyed via line 25 to a conventionalamplifier 23 whereafter it is filtered in filter 26. The circuitrybetween and including D/A converter 17 and filter 26 is designated forand typically employed in measuring the fine portion of the rotation ofthe rotor 3 with respect to the stator 2. In many typical applicationscoarse positions are measured by conventional additional converters andtransducers collectively represented by coarse position apparatus 39.

The coarse position apparatus 39 is typically connected between theup/down counter 15 via line 40 and the coarse/fine control 30 via line41. In operation, the coarse position circuitry operates until the rotor3 is within the range of the fine circuitry whereafter, in aconventional manner, the coarse positioning apparatus is disconnected bycoarse/fine control 30. Assuming for the purposes of the presentinvention that the coarse position apparatus 39 has been disconnected,the signals from the filter 26 pass straight through the coarse/finecontrol 30 via line 32 to a switch 33. Switch 33 is any conventionalswitch delivering, in the servo mode, the resultant signal (errorsignal) from filter 26 to appropriate drive apparatus 43 via a line 44.Drive apparatus 43 includes appropriate motor control circuitry and amotor for rotating the rotor 3 of position measuring transformer l andhence changing the space angle X. Drive apparatus 43 drives the rotor 3until the resultant signal on the lines 25 reaches a null (zerocondition) which occurs generally when the space angle X equals theelectrical angle Y. The rotor 3 becomes stationary when it assumes theposition commanded by computer 10.

In the readout mode of operation, switch 33 is switched so that theresultant signal from filter 26 via line 32 is connected via a line 47to an appropriate counter control 36. Counter control 36 suppliesdigital pulses and control signals to the up/down counter 15 via lines48 and 14 until the resultant signal is zero. In operation, the drive 43is typically energized, for example by a human operator via manual input8, to move the rotor 3 to a position to be measured as defined by someunknown space angle X and thereafter the rotor is mechanically locked inthat position while the measurement is performed. At the beginning ofthe measurement, the up/down counter 15 typically contains an arbitrarycount remaining from a previous use of the counter specifying anelectrical angle Y and that count is applied via line 16 through the D/Aconverter 17 to generate sine and cosine signals as a function of theelectrical angle Y. Those signals are supplied to the stator 2 via lines22. In general, the signals applied to stator 2, as a result of thearbitrary count, do not produce a null in the resultant signal on lines25 since the electrical angle Y does not equal the space angle X. When Xand Y are not equal, a resultant signal appears on line 25. Thatresultant signal is applied through the amplifier 23, filter 26, switch33, and control 36 to change the contents of the up/down counter 15. Achange in counter 15 changes, through D/A converter 17, the electricalangle Y of input signals on lines 22. The change in the electrical angleY continues until the output on line 25 is again a null which occurswhen, for the ideal case, Y equals X. When the output on line 25 is anull, signals are no longer applied via line 48 to the up/down counter15 (or alternatively line 14 causes a change in direction allowingcounter 15 to have a one count oscillation) so that the final contentsof the counter 15 are a measure of the space angle X of the rotor 3. Theelectrical angle Y is represented by the count registered in counter 15and is communicated to the computer and to the display 12 via line 13.That count is typically recorded in the computer for future use.

For further details of the operation of a position measuring transformerin systems having servo and readout modes, the above-referenced US. Pat.No. 3,514,775 is hereby incorporated by reference in this application.Specifically, FIG. 9 therein (and the description thereof) depict anup/down counter 124 (underlined numbers refer to references in the US.Pat. No. 775 analogous to counter herein where the input from 1500corresponds to line 48, and the output to elements 12, 30, and 38correspond to line 16. The outputs from stator drivers 126 correspond tolines 18 and 19 and the output from 120 to line 25.

Computer 10 is a conventional digital computer including meanS 4 forrecording the digital counts representing the electrical angles Ysupplied via line 13, including means 5 for averaging the recordedvalues, including means 6 for subtracting the recorded values, andincluding control means 7. Control means 7 functions to supply a commandinput to counter 15 via line 11 and a group selection input via line 9to control the operation of group selector 21. The operations ofcomputer 10 are all conventional and are conviently implemented with anIBM 1800 digital computer.

Before referring to the operation of the switching and coupling network20 and the group selector 21 which embody the group selection featuresof the present invention, a more detailed reference to the positionmeasuring transformer 1 is useful.

Position Measuring Transformer A typical but simplified embodiment ofthe position measuring transformer l of FIG. 1 is shown in schematicdetail in FIG. 2. Referring to FIG. 2, the continuous winding 51represents the winding forming part of the rotor 3 of FIG. 1. Similarly,in FIG. 2, the sine winding 54 and the cosine winding 55 represent thewindings forming part of the stator 2 of FIG. 1. Since FIG. 2 representsa top view, the winding 51 is shown by broken lines to designate that itis in a plane below the windings 54 and 55. Winding 51 includes 12conductor bars R1, R2, R12 which extend radially along imaginary linespassing through the center 0 of the winding 51. The conductor bars R1through R12 are interconnected by outer conductors 59 and innerconductors 59' into six series connected winding sections which beginand end with terminals 56 and 57. The conductors 59-59 interconnectingthe conductor bars Rl-R12 are non-inductively related, in accordancewith well-known principles, to the stator windings and hence they may beignored.

Like the continuous winding 51, the sine winding 54 is formed withinterconnected active conductor bars including eight conductor bars, S1,S2, S8 which are also located along imaginary radial lines passingthrough the center 0 of winding 54. Each pair of conductor bars, S1 andS2, S3 and S4, S7 and S8, is formed into a winding section so thatwinding sections SI, SH, SIH, and SIV, respectively, are fonned. Thesine winding 54, typically in the prior art, has its conductor bars andwinding sections serially interconnected between terminals T1 and T9,where each terminal T1 to T8 appears at the inner end of a conductorbar, in the manner shown by dotted lines in FIG. 2. In accordance withthe present invention, however, the interconnections shown as dottedlines, between the terminals T2 through T9, are not made in theconventional manner but rather are connected to switches SGl, SG2, SG3,and SG4 shown and described in connection with FIG. 5 hereinafter.

In a similar manner, the cosine winding 55 includes eight conductor barsC1, C2, C8 terminating along the outer ends, respectively, in terminalsD1, D2, D8. As with the sine winding, the cosine windings are connectedinto winding sections CI, CII, CHI, and CW which are in turn connectedin series as shown by the dotted lines in FIG. 2 between terminals. Inaccordance with the present invention, the winding sections CI, CH, CHI,and CIV are connected to switches CGl, CG2, CG3, and CG4 shown anddescribed hereinafter in connection with FIG. 5.

FIG. 3 is an edge view of the windings of FIG. 2 wherein the rotor 3having the winding 51 and the stator 2 having the windings 54 and 55 areshown to be parallel while forming an axis 66 through their respectivecenters 0 and 0 normal to the rotor.

FIG. 4(a) is a representation of the rotor and stator of FIG. 2 in whichthe rotor and stator centers have been shifted along the eccentricityaxis E-E' (referring to FIG. 2) by an amount e.In FIG. 4(a), the rotorplane 3 and the stator plane 2 remain parallel so that no skew exists.

FIG. 4(b) depicts the position measuring transformer of FIG. 2 whereinthe stator 2 has been skewed so that it is not parallel to the rotor 3.The centers 0 and 0' still form an axis normal to the rotor.

FIG. 4(0) depicts the position measuring transformer of FIG. 2 whereinboth the eccentricity of FIG. 4(a) and the skew of FIG. 4(b) have beenintroduced so that a line through the rotor and stator centers is notnormal to the rotor and the planes of the rotor and stator are notparallel.

For the position measuring transformer of FIG. 2, the total number, M,of pairs of winding sections on the stator 2 is four; namely, the pairsSI and CI, SH and CH, SIH and CHI, and SW and CIV. For convenience, atypical pair (e.g. SI and CI) of sine and cosine sections may beidentified as the m"' pair of sections where m may have any value from 1to M. For example in FIG. 2, m=l designates sections SI and CI, m=2designates sections 811 and CI], and so forth.

Before describing the operation of the FIG. 1 circuit and the manner inwhich it overcomes errors introduced by eccentricity, skew and otherconditions similar to those represented by FIGS. 4(a) through 4(0), ananalysis of the expected errors from such conditions is useful.

The following error analysis is presented in order to mathematicallyexplain the differences between measurements made with ideal positionmeasuring transformers and measurements made with transformersexhibiting skew only, exhibiting eccentricity only, and exhibitingeccentricity plus skew together. For an ideal position measuringtransformer, an electrical energization of the sine and cosine windingsof the stator causes the resultant signal (error signal) in the rotorwinding to null at a certain space angle X. If the rotor is rotated toan angle different from X, then of course, a non-null resultant signalis generated.

When the condition of skew alone is introduced into the afore-mentionedenergized, ideal transformer, the transformer still is operative to nullat the identical space angle, namely at X. The reason that skew alonedoes not alter the space angle at which the transformer nulls isbecause, for each change in the coupling (appearing as a gain changeresulting from the air gap change) caused by the displacement of awinding section of one type (e.g. sine), there is a corresponding andcompensating coupling change caused by an adjacent winding section ofthe opposite type (cosine).

In a similar manner, when the condition of eccentricity alone isintroduced into the afore-mentioned energized, ideal transformer, thespace angle at which the transformer nulls is again identical to X. Thereason that eccentricity alone does not alter the space angle at whichthe transformer nulls is that for each change in coupling (due to ashift resulting from eccentricity) caused by the displacement of astator winding section of one type (e.g. sine), an equal but oppositechange in coupling (due to an equal but electrically opposite shift) iscaused by the displacement of a stator winding section of the same type(sine) located 180 in space therefrom.

In summary, the effects of skew along are compensated by equal changesin coupling of adjacent winding sections of opposite type (sine andcosine), and the effects of eccentricity alone are compensated by equalbut opposite changes in coupling of 180-spaced winding sections of thesame type (sine and cosine. As discussed in more detail hereinafter, thecompound effects of skew and eccentricity, however, arenot compensatedgiving rise to errors. With these errors, the resultant signal does notnull at the ideal space angle X, but at that angle X modified by someerror angle.

The reason that the compound effects of skew and eccentricity are notcompensated, in the general case, is that the winding sections spacedapart by 180, which normally cause equal but opposite changes incoupling as a result of eccentricity, have their couplings unequallymodified as a result of skew so that the changes in coupling do not sumto zero. As a special case, these changes do sum to zero when theeccentricity axis E-E and the skew axis 8-8, to be described in furtherdetail hereinafter, are orthogonal.

Error Analysis For a typical position measuring transformer, similar tothat of FIG. 2, the signal, R induced in the single winding 51 of therotor by each m'" pair of sine and cosine stator winding sections isgiven as follows:

R,,,= Us sin (X,,,) Uc,, cos (z,,,) where:

Us, amplitude proportional to signal applied to stator sine winding(between terminals T1 and T9 of FIG. 2) Uc,,, amplitude proportional tosignal applied to stator cosine winding (between terminals D3 and D9 ofFIG. 2)

X, space angle of m' stator sine winding section with respect to cycleof rotor winding sections 2,, space angle of m"' stator cosine windingsection with respect to cycle of rotor winding sections The totalsignal, R, on the rotor (for example between terminals 56 and 57 of FIG.2) is derived from Eq. l as follows:

M M R= 2R E Us sin (X,,,) Uc cos (Z where:

M total number of pairs of sine and cosine winding sections Evaluating Rusing Eq. (2) where no errors are introduced and where the stator sinewindings are energized with an electrical signal D (cos Y) (sin wt) andthe stator cosine windings are energized with an electrical signal-D(sin Y)(sin wt), Us,, and Uc,, of Eq. (1) become,

Uc,, (B,,,)(-D sin Y sin wt) where:

sin wt= the carrier term Y= the electrical angle D amplitude A thetransfonnation factor for sine windings B,, =the transformation factorfor cosine windings No Skew and No Eccentricity For the condition whereno skew exists, A, B A for all in since the air gap between rotor andstator is a constant. Similarly with no eccentricity, Z,, X X for all msince there is a constant and equal rotation of the sine and cosinewinding sections of the stator with respect to the rotor. With theseassumed non-error conditions giving rise to the constant values A and X,Eq. 2) becomes,

R= (D sin wt) (sin Xcos Y- cos Xsin Y) (MA) R=(Dsin wt) (sin (X-Y)) (MA)E (5) As is apparent from Eq. (5 the null condition, R 0, is met whereno error conditions exist when the electrical angle Y equals the spaceangle X.

Eccentricity Alone When there is a relative shift between the rotor andstator centers, as generally depicted in FIG. 4(a), the condition 2,, XX for all m assumed above is no longer valid. By way of explanation andreferring to FIG. 6, assume the stator center 0 is shifted along theeccentricity axis E-E by an amount e" relative to the rotor center 0. Asa good approximation, that shift has the effect of rotating each windingsection, relative to its position before its shift, as a function of thesections angle, relative to the eccentricity axis E-E'.

Referring to FIG. 6, winding sections before shift are shown solid andafter shift, broken. Particularly typical stator winding sections 82,83, 84 and (shown solid) are symmetrical about their center 0 which isalso the center of the rotor winding (not shown). After shift thewinding sections 82', 83', 84' and 85 (shown broken) have center 0shifted e" from 0' along axis E-E. With respect to the center 0', theposition of the winding section 82 appears rotated by an angle d whered" is approximately e"/r when r is the average radius of the windingsection 82'. Similarly, the position of winding section 83' appearsrotated d" with respect to section 83. The position of the windingsections 84' and 85 along the eccentricity axis E-E' do not appearrotated.

Expressions for the m" sine sections apparent rotation, S,,,, and forthe m" cosine sections apparent rotation, C,,,, as a function of the m"sine sections angle, 45 with respect to the eccentricity axis EE' are,

S,,, (d) sin 4 Eq. (3) Eq. (4)

An evaluation of Eq. (2) when eccentricity alone is introduced is doneusing Eq. 3) and Eq. (4), still assuming A B for all m (since the airgap remains constant) but using X,, X S,, and Z,, X C,,, for sine andcosine terms, respectively, in accordance with Eqs. (6a) and (6b).

Note that there is a 180 symmetry of sine windings and of cosinewindings as described for typical windings in connection with FIG. 6,for each of the values of X, and Z,,. in Eq. (2). That condition alsoexists for the transformer of FIG. 2. For example, with m l andconsidering the sine terms only X =X+S andX ,=XS, andsoonuntil X ,,=X+8, and X =X S This plus and minus relationship is identical for thecosine terms and gives rise to the following form for Eq. (2):

M/2 R: 2 Us (sin (Xi-S +sin (XS =1 2M Us (cos (X+C )+cos (XC In" (21/8sin X cos (S,,,)-|-2Uccofi X cos (C,,,))

Since to a very good approximation M/2 2 Cos (Sm): E Cos (C m=l m=1 Eq.7 becomes, M

It (Us sin X-I-Uc cos X) (22 cos S Eq. (8) In a. manner analogous to Eq.(5), Eq. (8) becomes,

' M/2 R: (D sin wt) (sin (XY)) (2A 2 cos (S Comparing Eq. (5) withouteccentricity and Eq. (9) with eccentricity reveals that positionmeasuring transformers with eccentricity, as represented by FIG. 4(a),null at the same position as those without eccentricity (FIG. 3), thatis R when the space angle X equals the electrical angle Y.

Skew Alone When there is an introduction of skew alone, as generallydepicted in FIG. 4(b), the condition that the transformation factors A,,and B, are the same and equal to A for all sections (all m) is no longervalid. By way of explanation and referring to FIG. 7(a) four typicalstator winding sections 92, 93, 94 and 95 are shown. When those windingsections 92-95 are parallel to the rotor 3 as when in a plane like plane97 of FIG. 7(b), the transformation factor is constant because the airgap between rotor and stator is constant. However, when in a planeskewed to the rotor like plane 98, the average air gap for sections 93'and 95' is g-kl and g+kl, respectively, where g is the gap of anon-skewed plane and where kl is the average maximum direction from g ofthe winding sections as measured from the mid-points 99 and 100 ofsections 93' and 95, respectively. For winding sections 92 and 94 alonga line 8-8, called the skew axis, parallel to the rotor 3, the gap is g.

In the general case the gap of sine sections, Gs,,,, and cosinesections, Gc,,,, are given by Ge, =g- (kl) sin (4),, 360/M) where,

g the gap of a non-skewed plane (kl) the average maximum deviation fromg of winding sections 4 the angle of the m"' sine section from the skewaxis With the above expressions for the air gap, expressions for thetransformation factors A and B,,, are given by It is evident from Eqs.(10a) and (10b) that A and 13,, do not equal a constant A for allwinding sections, that is, for all m. However, for a large number ofwinding sections, that is for large M, A, does to a good approximationequal B... for each value of in since sin 4: and sin (d: 360/M) areapproximately equal for large M.

Evaluating Eq. (2) with A, B, for each value of m and st ssa X yields,

M R: 2 (B D cos Y sin wt sin X B D sin Y sin wt cos X) M R=(D sin wt)(sin (XY)) B Comparing Eq. l l with Eqs. (5) and (9) indicates that theintroduction of skew along produces a null (R 0) when the electricalangle Y equals the space angle X in the same manner as with eccentricityalone, Eq. (9), and without either skew or eccentricity, Eq. (5

Skew Eccentricity While the separate effects of skew and eccentricityhave been shown to produce the same null result, the compound effects ofskew and eccentricity do not, absent the present invention, lead to thesame result. Evaluation of Eq. (2), when the compound skew andeccentricity conditions represented by FIG. 4(c) are present, is asfollows:

R=D sin wt 2 (A cos Y sin X B sin Y cos Z M R=D sin wt 213 cos Y sin(X+S B sin Y cos (X+S M R=(D sin wt) EB sin (XY) cos S =1 m +B cos (XY)sin S It is evident from Eq. (13) that the null condition (R=0) is notachieved when X=Y as desired because, in the most righthand term, cos(X-Y) is not zero. That right-hand term, therefore, is essentially anerror term. The condition for R=0 in Eq. 12) is met when B sin (X-Y) cosS 2 E cos (X Y) sin S m=1 m=1 B sin S sin (XY) m=1 cos (XY) (X Y) TW 2 Bcos S 1n=1 M 2 13 sin S m=1 2 E cos S As will be discussed hereinafterin more detail, the present invention is directed to group operation ofwinding sections for reducing the difference between X and Y in order toachieve a null in the presence of the compound effects of skew andeccentricity. The group operation of winding sections is implemented inone embodiment using switching circuitry to select the winding sectionson a group by group basis to reduce the effects of skew andeccentricity.

Group Switching and Coupling Networks FIG. depicts the switching andcoupling network 20 of FIG. 1 in further detail as controlled by groupselector 21. In FIG. 5, the sine lines 18, and the cosine lines 19derived from the D/A converter 17 of FIG. 1 are connected to theswitching and coupling network 20. Sine lines 18 are connected inparallel to double pole switches SG1, SG2, SG3, and SG4 which in turnare connected through coupling transformers 76 to the sine windings atthe appropriate terminals Tl through T8, corresponding to conductor barsS1 through S8, respectively (see FIG. 2). In a similar manner, thecosine lines 19 are connected through double pole switches CGl, CG2, CG3and CG4 via independent coupling transformers 76 to the respectivecosine terminals D1 through D8, connected respectively to conductor barsCl through C8 (see FIG. 2). The sine and cosine windings aremagnetically coupled to the rotor winding 59 which includes theconductor bars R1 through R12 serially connected and terminating inlines 25.

The switches SG1 through SG4 and CGI through CG4 are energized undercontrol of a group selector 21. Group selector 21 may be conventionaldouble pole mechanical switches which open and close the double polecontacts of the switches SG1 through 804, and CGI through CG4. In analternative arrangement, the switches may be electronic, such astransistor driven mercury-wetted contacts, energized in a conventionalmanner by computer 10. In a typical operation, the sine switches andcosine switches are energized in pairs. For example, SG1 and CGI areinitially closed as shown in FIG. 5 with all of the other switches inthe open condition. With this closure of switches, the winding groupincluding winding sections SI and CI is energized while all of the otherwinding groups are not energized. With SG1 and CGI closed, the windingsections SI and CI magnetically couple the rotor winding 59 to produce aresultant signal on lines 25 as a function of the space angle X of therotor winding 59 with respect to stator windings 54 and 55.

Switch SG1, like each of the other switches of FIG. 5, is connectedthrough its own transformer 76 and its own balanced grounding network(pair of substantially equal resistors tied to ground) to the sinewinding section SI. Alternative grounding may be implemented by usinggrounded center-tapped windings for each of the secondaries oftransformers 76.

After the resultant signal on the lines 25 has been reduced to nulleither by changing the space angle X through rotating the rotor winding59 or by changing the electrical angle Y through altering the sine andcosine signals on lines 18 and 19, the first group of windings arede-energized by opening switches SG1 and CGI. Thereafter, the secondgroup of windings including winding sections 5]] and CH are energized byclosing switches S62 and CG2. Again the signal on the rotor winding 59is reduced to a null and thereafter the switches SG2 and CG2 arede-energized and the next group of windings are energized by closingswitches 5G3 and CG3. Thereafter, in a similar manner, the remainingswitches SG4 and CG4 are energized.

When it is desired to operate the stator windings 54 and 55 with all ofthe winding groups simultaneously closed switches SG1 through 504 andCGI through CG4 are closed. Such simultaneous operation has all of thewinding groups connected in parallel to the sine and cosine lines 18 and19. Alternatively, appropriate switching (not shown), may be employed toconnect all the sine conductor bars S1 through S8 and all the cosineconductor bars Cl through C8 in series. All connections whether serialor parallel are under control in a conventional manner by group selector21.

Group selector 21, in a preferred embodiment, is a plurality oftransistor inputs controlled by computer 10 via line 9 and the switchesSG and CG are transistors receiving the inputs. Computer 10 functions tocontrol the base (or gate) current in the transistors, therebyimplementing the switching and group selection functions in aconventional manner. Alternatively, the group selector 21 may be toggleson the mechanical double-pole switches depicted in FIG. 5.

Error Analysis With Group Operation As previously indicated inconnection with Eq. (13), the compound effects of skew and eccentricityon the resultant signal R normally prevent that signal from being equalto 0 when the space angle X equals the electrical angle Y. In accordancewith the present invention, however, individual groups of windingsections are separately energized and the signal on the rotor isseparately nulled so that the effects of skew are to a very goodapproximation eliminated from the resultant measurement. For example, ifeach pair of winding sections is separately energized, then Eq. (15)above reduces to a calculation of the difierence in space and electricalangles (X Y) for each value of m as follows:

It is evident from Eq. (16) that the space angle X differs from theelectrical angle Y by a term S,,,. If the separate measurements of X,,,for all m are averaged to form X the error terms 8,, averaged over all mbecome 0 so that the resultant is that X equals Y. It is evident thatS,, will average to 0 for the same reasons as previously discussed inconnection with the error analysis under the condition of eccentricityalone. More specifically, for each value of m between 1 and M12, thereis an equal and opposite value of S,,, for the 180 symmetry points ofS,,,, that is, for values of m equal to (M/2+l through M, respectively.

For purposes of explanation, consider the position measuring transformerof FIG. 2. When m equals l, the winding sections SI and CI of the firstgroup are rendered operative by switches SG1 and CGI in the apparatus ofFIG. 1 and FIG. 5. The value of the space angle X measured by theoperation of the FIG. I circuitry in the readout mode considering Eq.16) is as follows:

The value of S in Eq. (17) is (d) sin as derived from Eq. (6a).Accordingly and in a similar manner, the values X X X and X derived foreach of the four groups of winding sections of FIG. 2 are given asfollows:

X, Y+ (d) sin b, Eq.

(18-1 x,= Y+ (d) sin h, Eq.

(IS-2 X Y- (d) sin I E 18-3 X Y-- (d) sin 1 E It is evident that theadding and averaging of the above four equations yields a condition thatthe average value, X of the space angle values (X,, X X X is equal tothe electrical angle Y for measurements made at the null condition. Thisresult is identical to that previously derived for the no errorconditions of Eq. (5), the eccentricity alone condition of Eq. (9)andthe skew alone condition of Eq. l 1

Furthermore, if Eqs. (18-1) and (18-3) are subtracted, the resultantvalue is (2d) sin which is a measure of the eccentricity component alongan axis I III bisecting winding groups I and III at an angle dz, to theeccentricity axis E-E'. In a similar manner, subtraction of the Eq.l8-4) from Eq. 18-2) results in the value (2d) sin 4): which is ameasure of the eccentricity along an axis II IV bisecting the windinggroups II and IV at an angle D equal to 1 to the eccentricity axis 545'.

The addition, subtraction and averaging dictated by the above operationsis typically carried out using conventional algorithms in computer 10 ofFIG. 1.

Further and Other Embodiments While the number (M) of pairs of windingsections was four in the simplified transformer of FIG. 2, the number ofpairs of winding sections is typically much greater, for example, 1024.With this much larger number for M, the approximations relying on thecondition that 360/M was small become more valid (see Eq. (6b) etsequal). With M equal to 1024, 1024 different computations of X,, may beperformed and averaged to form X Rather than 1024 different measurementsof X,,,, however, it has been found that the employment of four windinggroups of 256 winding pairs per group provides excellent results. Whilesuch a technique of employing four groups does not theoreticallycompletely eliminate the compound effects of skew and eccentricity, theuse of four has enabled accuracies in measuring the space angle andmeasurements of eccentricity heretofore impossible.

FIG. 8 depicts another embodiment of the present invention in which aposition measuring transformer 101 has its rotor 103 energized in orderto induce signals in four groups of windings, I, II, III and IV ofwinding sections analogous to the groups described in connection withFIG. 2 and FIG. 5. The sine and cosine lines 129 and 130, respectively,from winding group I are connected to a sine/cosine computer network119.

The computer network 119 is typically like that described in the patentapplication Sine-Cosine Computer NETWORKS Ser. No. 704,900, filed2/12/68, by R. W. Tripp, assigned to the same assignee as the presentinvention. In that patent application, input sin X and cos X signals areapplied as inputs in the same manner as the present invention. Thecomputer network (like network 1 19) is operative to employ anotherangular input (therein designated and herein designated Y) to formoutput signals sin (X-Y) and cos (X-Y). In the present invention, onlythe sin XY) value is employed and it appears on output line 131.

Briefly, the computer network 119, as described in detail in theabove-identified patent application, functions to switch the taps ontransformer networks as a function of the input angle, Y. That Y angleis stored, in the present invention, in the Y counter 116 which hasoutputs 132 connected to the computer network 119 (through appropriateswitches not shown) to control and select the appropriate transformertaps which correspond to the Y angle.

A conventional oscillator 114 is connected via line 133 as an input tocounter 116 for the purpose of incrementing or decrementing counter 116in a direction controlled by the up/down (U/D) line 134. The U/D line134 is derived from a conventional phase detector 126. Phase detector126 receives the sine (X Y) signal on line 131. The other input to thephase detector 126 is a reference signal on line 135 derived through theconventional phase-shift circuit 112 (which balances any phase shiftattendant transformer 101 and network 1 19) from the signal applied tothe rotor on line 107.

In operation, the phase detector 126 controls line 134 either at abinary positive or negative level so as to cause incrementing ordecrementing of counter 116. Counter 116 in turn causes the computernetwork 119 to drive its output signal on line 131 to a null or zerocondition. such a null condition occurs when the space angle, X, equalsthe electrical angle, Y, in a manner analogous to that previouslydescribed in connection with the prior description of the presentinvention. When the count in counter 116 represents a value equal to thespace angle X, the next pulse from the oscillator 114 on line 133 causescounter 1 16 to be one count different from the value of the space angleX which in turn will cause the signal on line 131 to be one incrementallevel different from null which will in turn be detected by phasedetector 126 causing the U/D line 134 to change level so as to changethe direction of count of counter 116. Therefore, the next pulse fromoscillator 114 causes counter 116 to count in the opposite direction sothat X and Y are again equal. Further pulses from the oscillator 114again generate a signal on line 131 which will again cause the U/D line134 to reverse its level again causing X to equal Y.

Further details as to the operation of a phase detector in combinationwith an oscillator driven counter like that depicted in the electronicservo circuit 109 are described in the US. Pat. application, entitledTrigonometric Signal Generator And Machine Control having Ser. No.864,079, filed l0/6/69, invented by R. W. Tripp and assigned to the sameassignee as the present invention. That application is herebyincorporated by reference in this application for the purpose ofteaching the details of phase detector in combination with oscillatordriven counters. See specifically, FIG. 18, element 318 and attendantdescription therein.

The output from the counter 116 is conveyed via a line 137 to aconventional computer 110. Analogous to the electronic servo 109, eachof the winding groups, II, III and IV includes an identical electronicservo 109, 109", and 109", respectively. Each of those electronic servos109', 109", and 109" is connected via lines 137, 137", and 137",respectively, to the computer 110.

Each of the electronic servos functions to transmit to computer thevalue of the electrical angle Y as a measure of the space angle X foreach of the groups of stator windings I, II, III, and IV. Computer 110forms the average of these measured angles to form a group average, X ofthe space angle which is to a good approximation free of errors causedby the conditions of eccentricity and skew for the reasons previouslydescribed.

When a calculation has been rendered for some initial space angle, X,drive 140 may be operated to select a new space angle by rotating rotor103 whereafter each of the electronic servos 109, 109, 109", and 109"electronically servos to form new measurement angles Y. Thosemeasurement angles Y are again averaged in computer 110 to form themeasurement for X,,,,,.

Computer 110 may also be employed in a conventional manner to form thedifierence between the I and III winding groups and the II and IVwinding groups. As previously described, these different values aremeasures of the eccentricity components along the respective axes.

While the invention has been described principally with respect torotary positionmeasuring transformers, the method and apparatus areapplicable to linear position measuring transformers. For example, ifthe windings of a linear transformer exhibit a variable air gap, such asmay be caused by Inductosyn bar scales having discrete air gapdifferences from bar to bar or by Inductosyn tape scales exhibitingundulations along its length, an error causing condition analogous toskew in rotary devices exists. Similarly, if the direction of travel ofthe slider with respect to the scale is non-parallel to an axis runningthrough the scale lengthwise, an error condition analogous toeccentricity in rotary devices exists. With such error-causingconditions in linear transformers, the group energization techniques ofthe present invention are effective to minimize errors resulting fromthe compound effects of such conditions.

Although the present invention has been described employing theconvention that the space-quadrature windings are mounted, for rotarydevices, upon the stator and the single continuous winding is mountedupon the rotor and similarly that the space-quadrature windings aremounted, for linear devices, upon the slider and the continuous windingis mounted upon the scale, it is within the present invention that thespace-quadrature and single continuous windings be upon any of themembers. For the purposes of this application, the terms stator, rotor,slider, and scale are all interchangeable. While the invention appliesto conventional rotary and linear devices, it also applies to spiral orother type devices such as described in US. Pat. No. 2,900,612.

Although the present invention has been described in terms of positionmeasuring transformers which employ spacequadrature windings so as todescribe a sine/cosine two-phase system, it will of course be realizedthat three-phase or other polyphase systems may be employed within thespirit of the present invention. Similarly, while the present inventionhas been described for an amplitude sensitive system, the invention isequally applicable to phase sensitive systems.

While the invention has been particularly shown and described withreference to preferred embodiments thereof, it will be understood bythose skilled in the art that the foregoing and other changes in formand details may be made therein without departing from the spirit andscope of the invention.

What is claimed is:

l. A position measuring apparatus including first and second relativelymovable members, one of said members including a first winding ofperiodically spaced conductors which define a reference cycle, the otherof said members including at least one winding group having at least twospaced windings reactively coupled to said first winding for defining aspace angle as a function of the position of said spaced windingsrelative to said first winding, said apparatus including at least onesource of electrical signals defining an electrical angle to form atleast one measurement signal and further including means for nullingsaid measurement signal by rendering the space angle equal to theelectrical angle, the improvement comprising,

a plurality of independently operable winding groups on said other ofsaid members, each group including first and second spaced windingsections reactively coupled to said first winding, and each group spacedrelative to said first winding to define independently the same saidspace angle,

means for supplying electrical signals defining an electrical angleindependently for each of said winding groups to form a separatemeasurement signal for each of said winding groups,

means for independently nulling each of said separate measurementsignals for each of said winding groups.

2. The apparatus of claim 1 wherein said first winding sections arepositioned at periodic first locations and said second winding sectionsare positioned at periodic second locations in space-quadrature withrespect to said reference cycle.

3. The apparatus of claim 1 further including,

means responsive to said measurement signals for forming, for each ofsaid winding groups, a digital representation of the relative spaceposition of said members as measured by each of said winding groups.

4. The apparatus of claim 3 further including,

means for recording and averaging said digital representations to form aresultant digital representation of the relative space position of saidmembers.

5. The apparatus of claim 4 wherein said members are rotary in form andwherein there are four winding groups arranged to form four quadrants,respectively, on said other member.

6. The apparatus of claim 3 further including,

switching means for sequentially energizing said winding groups so as tosequentially produce said measurement signals and said digitalrepresentations.

7. The apparatus of claim 3 wherein said members are relatively rotable,wherein each winding group has an associated winding group located 180degrees about a first axis, and wherein said first winding isdistributed in a rotary pattern on said one member about a second axiswhere the second axis may exhibit some eccentricity with respect to saidfirst axis, said apparatus further comprising,

means for measuring said eccentricity between said first and second axesincludes means for subtracting the digital representation for eachwinding group from the digital representation for the 180 degreeassociated winding group.

8. The apparatus of claim 7 wherein the number of said winding groups isfour for obtaining two components, each along an axis orthogonal to theother, of the eccentricity between said first and second axes.

9. The apparatus of claim 2 wherein said winding groups aresymmetrically disposed in a rotary pattern on a stator and wherein saidfirst winding is disposed in a rotary pattern on a rotor forming aposition measuring transformer wherein the rotor forms a space angle Xwith respect to the stator, said apparatus further comprising,

means for independently energizing said first winding sections in eachwinding group with an electrical signal proportional to (A)sin(Y) andsaid second winding sections in each winding group with an electricalsignal proportional to (A)cos(Y) so as to induce a resultant signal insaid first winding proportional to (A)sin( X-Y),

means for changing one of the values X or Y while holding the othervalue fixed to reduce said resultant signal to a null and thereby toindicate that the changed value equals the fixed value.

10. The apparatus of claim 9 wherein,

said means for changing comprises a digital to analog converterincluding a digital counter registering said value Y and means forchanging the count in said digital counter to change the value of Y.

1 l. The apparatus of claim 10 further including a digital displayconnected to and operative to display the contents of said digitalcounter.

12. The apparatus of claim 2 wherein said winding groups aresymmetrically disposed in a rotary pattern on a stator and wherein saidfirst winding is disposed in a rotary pattern on a rotor forminga-position measuring transformer wherein the rotor forms a space angle Xwith respect to the stator, said apparatus further comprising,

means for energizing said first winding with a constant amplitude ACsignal whereby electrical signals of the form (A)sin(X) and (A)cos(X)are induced in each winding group,

computer network means responsive to said signals of the form (A)sin(X)and (A)cos(X) to produce a resultant signal proportional to (A)sin(X-Y),and

meanS for changing one of the values X or Y while holding the othervalue fixed to reduce said resultant signal to a null and to therebyindicate that the changed value equals the fixed value.

13. The apparatus of Claim 12 wherein,

said means for changing includes a digital counter for registering thevalue Y and wherein said digital counter and said computer network meansare responsive to said resultant signal.

14. A position measuring apparatus including,

a transformer having a rotor relatively movable with respect to a statorfor generating measurement signals as a function of electrical inputsignals functionally related to an electrical angle Y and as a functionof the relative space position of said rotor and stator as measured by aspace angle X, said rotor including a continuous winding having activeconductor bars defining a pole cycle, said stator including sine andcosine windings,

a digital-to-analog converter for energizing said sine winding with anelectrical signal functionally related to cos(Y) to produce a signalproportional to sin(X)cos( Y) and for energizing said cosine windingwith an electrical signal functionally related to sin(Y) to produce asignal proportional to cos(X)sin(Y) thereby forming a resultant signalin said continuous winding proportional to sin(X-Y) for controlling saiddigital-to-analog converter,

a digital counter for storing a digital representation of the electricalangle Y,

a counter control connected to receive said resultant signal and forcausing said digital counter to change its contents until said resultantsignal is a null,

a digital computer connected to said digital counter for recording thecontents of said digital counter each time a null condition is detected,the improvement comprising,

a plurality of independently operable winding groups on said stator,each group inductively coupled to said continuous winding, each groupincluding'a plurality of winding sections of sine and cosinesignificance in spacequadrature of the pole cycle of the continuouswinding, each alternate winding section of one significance for eachgroup interconnected to form a sine winding for inducing in saidcontinuous winding a signal related to sin(X), each other alternatewinding section of the other significance for each group interconnectedto form a cosine winding for inducing in said continuous winding asignal related to cos(X),

automatic switching means for sequentially energizing each of saidwinding groups with the signals from said digitalto-analog converter soas to form said digital representation of Y for each group and forrecording each digital representation of Y in said computer, and

means in said computer for averaging said recorded digitalrepresentations of Y in order to form a resultant measure of the spaceangle X.

15. The method of measuring the relative space angle X of the rotor withrespect to the stator of a position measuring device wherein the rotorincludes a single continuous winding,

and wherein the stator includes a plurality of winding groupstrlgonometrically related to the continuous winding, comprising theindependent performance for each of said winding groups of the followingsteps,

energizing the winding of a group with signals proportional totrigonometric functions of an electrical angle Y so as to induce aresultant signal in the continuous winding proportional to sin(X-Y),altering the electrical angle Y until a null condition is reached when Xequals Y, and recording a digital representation of Y when the nullcondition is reached to thereby form a measure of the value X. 16. Themethod of claim 15 further including the steps of, averaging saidrecorded digital representations to form a resultant value as a measureof the space angle X. 17. The method of claim 15 further including thesteps of, subtracting said recorded digital representations for windinggroups having position relationship to form a component measure of theeccentricity of the stator windings with respect to the rotor winding.

t i h l

1. A position measuring apparatus including first and second relativelymovable members, one of said members including a first winding ofperiodically spaced conductors which define a reference cycle, the otherof said members including at least one winding group having at least twospaced windings reactively coupled to said first winding for defining aspace angle as a function of the pOsition of said spaced windingsrelative to said first winding, said apparatus including at least onesource of electrical signals defining an electrical angle to form atleast one measurement signal and further including means for nullingsaid measurement signal by rendering the space angle equal to theelectrical angle, the improvement comprising, a plurality ofindependently operable winding groups on said other of said members,each group including first and second spaced winding sections reactivelycoupled to said first winding, and each group spaced relative to saidfirst winding to define independently the same said space angle, meansfor supplying electrical signals defining an electrical angleindependently for each of said winding groups to form a separatemeasurement signal for each of said winding groups, means forindependently nulling each of said separate measurement signals for eachof said winding groups.
 2. The apparatus of claim 1 wherein said firstwinding sections are positioned at periodic first locations and saidsecond winding sections are positioned at periodic second locations inspace-quadrature with respect to said reference cycle.
 3. The apparatusof claim 1 further including, means responsive to said measurementsignals for forming, for each of said winding groups, a digitalrepresentation of the relative space position of said members asmeasured by each of said winding groups.
 4. The apparatus of claim 3further including, means for recording and averaging said digitalrepresentations to form a resultant digital representation of therelative space position of said members.
 5. The apparatus of claim 4wherein said members are rotary in form and wherein there are fourwinding groups arranged to form four quadrants, respectively, on saidother member.
 6. The apparatus of claim 3 further including, switchingmeans for sequentially energizing said winding groups so as tosequentially produce said measurement signals and said digitalrepresentations.
 7. The apparatus of claim 3 wherein said members arerelatively rotable, wherein each winding group has an associated windinggroup located 180 degrees about a first axis, and wherein said firstwinding is distributed in a rotary pattern on said one member about asecond axis where the second axis may exhibit some eccentricity withrespect to said first axis, said apparatus further comprising, means formeasuring said eccentricity between said first and second axes includesmeans for subtracting the digital representation for each winding groupfrom the digital representation for the 180 degree associated windinggroup.
 8. The apparatus of claim 7 wherein the number of said windinggroups is four for obtaining two components, each along an axisorthogonal to the other, of the eccentricity between said first andsecond axes.
 9. The apparatus of claim 2 wherein said winding groups aresymmetrically disposed in a rotary pattern on a stator and wherein saidfirst winding is disposed in a rotary pattern on a rotor forming aposition measuring transformer wherein the rotor forms a space angle Xwith respect to the stator, said apparatus further comprising, means forindependently energizing said first winding sections in each windinggroup with an electrical signal proportional to (A)sin(Y) and saidsecond winding sections in each winding group with an electrical signalproportional to (A)cos(Y) so as to induce a resultant signal in saidfirst winding proportional to (A)sin(X-Y), means for changing one of thevalues X or Y while holding the other value fixed to reduce saidresultant signal to a null and thereby to indicate that the changedvalue equals the fixed value.
 10. The apparatus of claim 9 wherein, saidmeans for changing comprises a digital to analog converter including adigital counter registering said value Y and means for changing thecount in said digital counter to change the value of Y.
 11. Theapparatus of claim 10 further including a digital display connected toand operative to display the contents of said digital counter.
 12. Theapparatus of claim 2 wherein said winding groups are symmetricallydisposed in a rotary pattern on a stator and wherein said first windingis disposed in a rotary pattern on a rotor forming a position measuringtransformer wherein the rotor forms a space angle X with respect to thestator, said apparatus further comprising, means for energizing saidfirst winding with a constant amplitude AC signal whereby electricalsignals of the form (A)sin(X) and (A)cos(X) are induced in each windinggroup, computer network means responsive to said signals of the form(A)sin(X) and (A)cos(X) to produce a resultant signal proportional to(A)sin(X-Y), and meanS for changing one of the values X or Y whileholding the other value fixed to reduce said resultant signal to a nulland to thereby indicate that the changed value equals the fixed value.13. The apparatus of Claim 12 wherein, said means for changing includesa digital counter for registering the value Y and wherein said digitalcounter and said computer network means are responsive to said resultantsignal.
 14. A position measuring apparatus including, a transformerhaving a rotor relatively movable with respect to a stator forgenerating measurement signals as a function of electrical input signalsfunctionally related to an electrical angle Y and as a function of therelative space position of said rotor and stator as measured by a spaceangle X, said rotor including a continuous winding having activeconductor bars defining a pole cycle, said stator including sine andcosine windings, a digital-to-analog converter for energizing said sinewinding with an electrical signal functionally related to cos(Y) toproduce a signal proportional to sin(X)cos(Y) and for energizing saidcosine winding with an electrical signal functionally related to sin(Y)to produce a signal proportional to cos(X)sin(Y) thereby forming aresultant signal in said continuous winding proportional to sin(X-Y) forcontrolling said digital-to-analog converter, a digital counter forstoring a digital representation of the electrical angle Y, a countercontrol connected to receive said resultant signal and for causing saiddigital counter to change its contents until said resultant signal is anull, a digital computer connected to said digital counter for recordingthe contents of said digital counter each time a null condition isdetected, the improvement comprising, a plurality of independentlyoperable winding groups on said stator, each group inductively coupledto said continuous winding, each group including a plurality of windingsections of sine and cosine significance in space-quadrature of the polecycle of the continuous winding, each alternate winding section of onesignificance for each group interconnected to form a sine winding forinducing in said continuous winding a signal related to sin(X), eachother alternate winding section of the other significance for each groupinterconnected to form a cosine winding for inducing in said continuouswinding a signal related to cos(X), automatic switching means forsequentially energizing each of said winding groups with the signalsfrom said digital-to-analog converter so as to form said digitalrepresentation of Y for each group and for recording each digitalrepresentation of Y in said computer, and means in said computer foraveraging said recorded digital representations of Y in order to form aresultant measure of the space angle X.
 15. The method of measuring therelative space angle X of the rotor with respect to the stator of aposition measuring device wherein the rotor includes a single continuouswinding, and wherein the stator includes a plurality of winding groupstrigonoMetrically related to the continuous winding, comprising theindependent performance for each of said winding groups of the followingsteps, energizing the winding of a group with signals proportional totrigonometric functions of an electrical angle Y so as to induce aresultant signal in the continuous winding proportional to sin(X-Y),altering the electrical angle Y until a null condition is reached when Xequals Y, and recording a digital representation of Y when the nullcondition is reached to thereby form a measure of the value X.
 16. Themethod of claim 15 further including the steps of, averaging saidrecorded digital representations to form a resultant value as a measureof the space angle X.
 17. The method of claim 15 further including thesteps of, subtracting said recorded digital representations for windinggroups having 180* position relationship to form a component measure ofthe eccentricity of the stator windings with respect to the rotorwinding.